data(trees) head(trees)
Girth Height Volume 1 8.3 70 10.3 2 8.6 65 10.3 3 8.8 63 10.2 4 10.5 72 16.4 5 10.7 81 18.8 6 10.8 83 19.7
February 23, 2023
treesdata(trees) head(trees)
Girth Height Volume 1 8.3 70 10.3 2 8.6 65 10.3 3 8.8 63 10.2 4 10.5 72 16.4 5 10.7 81 18.8 6 10.8 83 19.7
trees; Volume vs Girth
model: \(\text{Volume} = \beta_0 + \beta_1\cdot\text{Girth} + \varepsilon; \hspace{1 cm} \varepsilon \sim N(0; \sigma^2)\)
 fitted: \(\text{Volume} = \hat{\beta_0} + \hat{\beta_1} \cdot \text{Girth}\)        \(\hat{\beta_0} = b_0 - \text{estimate of }\beta_0\); \(\hat{\beta_1} = b_1 - \text{estimate of }\beta_1\) <>
diamond from UsingRlibrary(UsingR) library(plotly) data(diamond) head(diamond)
carat price 1 0.17 355 2 0.16 328 3 0.17 350 4 0.18 325 5 0.25 642 6 0.16 342
mtcarsdata(mtcars) attach(mtcars)
The following object is masked from package:ggplot2:
mpg
head(mtcars)
mpg cyl disp hp drat wt qsec vs am gear carb Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4 Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4 Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1 Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1 Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2 Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1
xax = list(title="Weight",
titlefont=list(family="Modern Computer Roman"))
yax = list(title="Miles per Gallong",
titlefont=list(family="Modern Computer Roman"))
plot_ly(mtcars, x=wt, y=mpg, type="scatter", mode="markers", col=disp) %>% layout(xaxis=xax, yaxis=yax)
Warning: 'scatter' objects don't have these attributes: 'col' Valid attributes include: 'cliponaxis', 'connectgaps', 'customdata', 'customdatasrc', 'dx', 'dy', 'error_x', 'error_y', 'fill', 'fillcolor', 'fillpattern', 'groupnorm', 'hoverinfo', 'hoverinfosrc', 'hoverlabel', 'hoveron', 'hovertemplate', 'hovertemplatesrc', 'hovertext', 'hovertextsrc', 'ids', 'idssrc', 'legendgroup', 'legendgrouptitle', 'legendrank', 'line', 'marker', 'meta', 'metasrc', 'mode', 'name', 'opacity', 'orientation', 'selected', 'selectedpoints', 'showlegend', 'stackgaps', 'stackgroup', 'stream', 'text', 'textfont', 'textposition', 'textpositionsrc', 'textsrc', 'texttemplate', 'texttemplatesrc', 'transforms', 'type', 'uid', 'uirevision', 'unselected', 'visible', 'x', 'x0', 'xaxis', 'xcalendar', 'xhoverformat', 'xperiod', 'xperiod0', 'xperiodalignment', 'xsrc', 'y', 'y0', 'yaxis', 'ycalendar', 'yhoverformat', 'yperiod', 'yperiod0', 'yperiodalignment', 'ysrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'
Warning: `line.width` does not currently support multiple values. Warning: `line.width` does not currently support multiple values. Warning: `line.width` does not currently support multiple values.
\(X \sim N(\mu=30, \sigma^2=5^2); Y \sim N(0,1); Z \sim N(15, 2^2); color = Z\)
\(X, Y, Z - independent\)
set.seed(123) myX = rnorm(100, mean=30, sd=5) myY = rnorm(100) myZ = rnorm(100, mean=15, sd=2)
plot_ly(x=myX, y=myY, z=myZ,
type="scatter3d", mode="markers",
color=myZ) %>%
hide_colorbar()
\(f(x,y)=sin(x+1)+y^2\) and \(f(x,y)=0.6x + 8\)
x = seq(-6, 6, 0.5)
y = seq(-2, 2, 0.5)
X = matrix(rep(x, length(y)), nrow=length(y), byrow=T)
Y = matrix(rep(y, length(x)), ncol=length(x), byrow=F)
Z = sin(X+1) + Y^2
Zp = 0.6*X + 0.8
fig = plot_ly(x=X, y=Y, z=Z, showscale=F, width=800, height=550) %>%
add_surface(contours=list(
z=list(show=T,
usecolormap=T,
highlightcolor="#ff0000",
project=list(z=T)
)
)
)
fig = fig %>% layout(list( scene=list(camera=list(eye=list(x=1.87, y=0.88, z=-0.6))) )) %>% add_surface(z=Zp) fig
\(\cdot, x^2, x^{22}, x_a^{22}, x_{ab}^{22}\) \(\bar{x}, \bar{x}_n, \hat{\Theta}\) \(\alpha, \beta, \gamma, \epsilon, \varepsilon, \phi, \varphi, \chi^2\) \(\displaystyle MSE = {SSE\over n-2} \sum_{i=1}^n (y_i - \hat{y}_i)^2\) \(Hello \hspace{3cm} There\)
plot(mtcars$mpg, mtcars$cyl)
Scatter plot